Finite Volume Method and Accuracy of Groundwater Flow Models

摘要

The accuracy and reliability of numerical models rely on the minimization of errors and uncertainties. In groundwater modelling there are three sources of errors, namely conceptual errors, numerical errors and errors resulting from uncertainties or lack of input data. These errors can occur during the model development or application. The finite volume method has several numerical advantages. Groundwater models based on this method involve the approximation of the hydraulic gradient at cell faces. An overview of different methods for approximating the gradient on a control volume face is given. A finite volume groundwater flow model based on flux approximation using decomposed vectors is presented. Errors related to numerical diffusion and the mesh are evaluated. Numerical tests on the model accuracy in solving diffusion equations and its sensitivity to the mesh size, non-orthogonality and skewness are presented. The model results are then compared with the analytical solutions and the finite difference solutions. The results show the robustness of the developed model and the accuracy of the selected gradient approximation on asymmetric and non-orthogonal grids.